Depending on your location and the weather conditions that you drive in there are three classes of tyre to consider, summer, all season and winter tyres.
If you are unlikely to spend much time driving on snow or ice summer tyres would suffice. (Primacy)
If you live in an area which gets a decent amount of ice and snow they might be better replaced with all season tyres. (Cross climate)
If you live in the highlands and get regular snow and ice, winter tyres are slightly better than all season, (Alpin) but the gap between all season and winter tyres is getting smaller and they are a very good alternative.
If you are likely to take your car to Europe in the winter, some countries such as Austria specify winter/all season tyres and a minimum tread depth. Others such as Germany recommend winter or all season tyres but they are not a legal requirement (yet), however should you be involved in an accident you would regret not having them. I mention Germany as we have family members there who up until recently stored their winter tyres in a "tyre hotel" and only had one set of wheels, but have swapped to all seasons.
Summer tyres are designed for longevity and water clearance with a less blocky tread pattern, but start to harden below 7 degrees and loose efficiency.
Winter and all season tyres have a blocky tread designed to fill with snow as snow sticks to snow and they do not harden as the temperature gets below 7 degrees. The blocky tread means they do not clear water quite as well as summer tyres. Winter/all season tyres are not necessarily better in wet mud as the treads will fill with slippery mud and could slip/spin even on a four wheel drive.
AT/all terrain/off road tyres are a different matter with aggressive self cleaning tread patterns and can be noisy and fuel hungry, don't go there.